Maximum entropy analysis of binary variables provides an elegant way for studying the role of pairwise correlations in neural populations [1,2]. Unfortunately, these approaches suffer from their poor scalability to high dimensions. In sensory coding, however, high-dimensional data is ubiquitous. Here, we introduce a new approach using a near-maximum entropy model, that makes this type of analysis feasible for very high-dimensional data - the model parameters can be derived in closed form and sampling is easy. We demonstrate its usefulness by studying a simple neural representation model of natural images. For the first time, we are able to directly compare predictions from a pairwise maximum entropy model not only in small groups of neurons, but also in larger populations of more than thousand units. Our results indicate that in such larger networks interactions exist that are not predicted by pairwise correlations, despite the fact that pairwise correlations explain the lower-dimensional marginal statistics extremely well up to the limit of dimensionality where estimation of the full joint distribution is feasible.

[1] E Schneidman, MJ Berry, R Segev, and W Bialek. Nature, 440:1007-1012 (2006).
[2] J Shlens, JD Field, JL Gauthier, MI Grivich, D Petrusca, A Sher, AM Litke, and EJ Chichilnisky. J Neurosci, 26:8254-8266 (2006).